Barrie signed a one-year, $3.75 million contract with the Oilers on Saturday.
Barrie (undisclosed) suffered concussion-related symptoms after hitting his head on the ice in Game 5, telling reporters, "I banged my head on the ice pretty hard and had some headaches. They're pretty careful with the concussion stuff. Thankfully I'm feeling pretty good right now but I had to take care of it," NHL.com's Dave McCarthy reports.
Barrie sustained an undisclosed injury in the second period of Sunday's Game 5 against Columbus and will not return.
Barrie delivered two more assists in a 4-2 win over Vancouver on Saturday.
Barrie posted an assist at even strength and on the power play along with a plus-1 rating, two hits, one shot and one block in a 4-3 victory over the Lightning on Tuesday.
Barrie picked up two assists Saturday in a 6-3 loss to Carolina.
Barrie fired six shots on net and went minus-1 in Tuesday's 5-2 loss to the Penguins.
Barrie finished Wednesday's 5-3 win over Dallas with two points.
Barrie produced an assist and went minus-3 in Sunday's 8-4 loss to the Panthers.
Barrie had his five-game point streak snapped Saturday against the Islanders.